Gravitational collapse and structure formation in an expanding universe with dark energy

TL;DR

This paper investigates how dark energy, modeled as a cosmological constant, influences the collapse of spherical over-densities, revealing a minimum density threshold for collapse and extended collapse times.

Contribution

It introduces a detailed analysis of structure formation in a universe with dark energy, identifying a critical over-density threshold for collapse.

Findings

A minimum over-density is required for collapse in a dark energy universe.

Perturbations near the threshold take a very long time to collapse.

Dark energy delays or prevents collapse of certain over-densities.

Abstract

Observations show that the expansion of the Universe is accelerating. This requires that the dominant constituent of matter in the Universe has some unusual properties like negative pressure. This exotic component has been given the name dark energy. We work with the simplest model of dark energy, the cosmological constant introduced by Einstein. We study the evolution of spherical over-densities in such a model and show that there is a minimum over-density required for collapse: perturbations with a smaller amplitude do not collapse. This threshold is interesting as even perturbations with a positive over-density and negative energy do not collapse in finite time. Further, we show that perturbations with an amplitude larger than, but comparable to the threshold value, take a very long time to collapse. We compare the solutions with the case when dark energy is absent.